Pump-Dump Excitation with Many Levels Tannor-Rice Scheme

1 PUMP-DUMP EXCITATION WITH MANY LEVELS TANNOR-RICE SCHEME 

Equation (4.4) has the qualitative interpretation that Ef evolves on the ground state surface until time t = t2 when it makes a transition to the excited electronic surface. It then propagates for a time t2 to tx at which time it makes a transition back to the ground electronic state. The wave function then evolves on the groimd state surface until time t when we measure its overlap with the product state. Since the fields are spread out over time, we have to integrate over both /, and t2. 

As in Section 3.5, e(z, t) is often comprised of two temporally distinct pulses, where the timing between the two pulses serves as a control parameter. It is interesting to examine, for example, the limiting case where i (z, t) comprises two delta function pulses. In this case the pulses have an infinitely wide profile in frequency, space and hence encompass a complete set of levels. This is the extreme opposite of the case discussed in Section 3.5 where the laser pulse only encompasses two levels. Here, neglecting the spatial dependence, the field is of the form i 

in this case, the ratio of product into various arrangement channels controlled entirely by the time delay (td — tx) between pulses. 

This example also makes clear that (f x and f)d, the phases of the two pulses not enter the final expression, a result that holds true even for pulses of finite 

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